Observation of the Resonance Frequencies of a Stable Torus of Fluid.

We report the first quantitative measurements of the resonance frequencies of a torus of fluid confined in a horizontal Hele-Shaw cell. By using the unwetting property of a metal liquid, we are able to generate a stable torus of fluid with an arbitrary aspect ratio. When subjected to vibrations, the torus displays azimuthal patterns at its outer periphery. These lobes oscillate radially, and their number n depends on the forcing frequency. We report the instability "tongues" of the patterns up to n=25. These resonance frequencies are well explained by adapting to a fluid torus the usual drop model of Rayleigh. This approach could be applied to the modeling of large-scale structures arisen transiently in vortex rings in various domains.